二叉树的应用（南邮数据结构实验二）

  1 #include<iostream>
  2 using namespace std;
  3 template<class T>      
  4 struct BTNode          // 结点类
  5 {
  6     BTNode()
  7     {
  8         lchild=rchild=NULL;
  9 
 10     }
 11     BTNode(const T &x)
 12     {
 13         element=x;
 14         lchild=rchild=NULL;
 15     }
 16     BTNode(const T &x,BTNode<T> *l,BTNode<T> *r)
 17     {
 18         element=x;
 19         lchild=l;
 20         rchild=r;
 21 
 22     }
 23     T element;
 24     BTNode<T>* lchild,*rchild;
 25 };
 26 template<class T>
 27 class BinaryTree
 28 {
 29 public:
 30     BinaryTree()
 31     {
 32         root=NULL;
 33     }
 34     ~BinaryTree()
 35     {
 36         delete []root;
 37     }
 38     bool Root(T &x)const;
 39     void MakeTree(const T &x,BinaryTree<T> & left,BinaryTree<T> &right);
 40 
 41     void BreakTree(T &x,BinaryTree<T> & left,BinaryTree<T> &right);
 42  // void Visit(T &x);
 43     void PreOrder(void (*Visit)(T &x));
 44     void PreOrder(void (*Visit)(T &x),BTNode<T> *t);
 45     void InOrder(void (*Visit)(T &x));
 46     void InOrder(void (*Visit)(T &x),BTNode<T> *t);
 47     void PostOrder(void (*Visit)(T &x));
 48     void PostOrder(void (*Visit)(T &x),BTNode<T> *t);
 49 
 50     int Size();
 51     int Size(BTNode<T>*t);
 52     int Node_num(BTNode<T>*p) ;
 53     BTNode<T>* Copy(BTNode <T>*t);
 54     int High(BTNode<T>*p);
 55     void Exchange(BTNode<T>*&t);
 56 
 57     BTNode<T> *root;
 58 };
 59 template<class T>
 60 bool BinaryTree<T>::Root(T &x)const
 61 {
 62     if(root)
 63     {
 64         x=root->element;
 65         return true;
 66     }
 67     else 
 68         return false;
 69 }
 70 template<class T>
 71 void BinaryTree<T>::MakeTree(const T &x,BinaryTree<T> & left,BinaryTree<T> &right)
 72 {
 73     if(root||&left==&right )
 74         return ;
 75     root=new BTNode<T>(x,left.root,right.root);
 76     left.root=right.root=NULL;
 77 }
 78 
 79 template <class T>
 80 void BinaryTree<T>::BreakTree(T &x,BinaryTree<T> & left,BinaryTree<T> &right)
 81 {
 82     if(!root||&left.root==&right.root||left.root||right.root)
 83         return;
 84     x=root->element;
 85     left.root=root->lchild;
 86     right.root=root->rchild;
 87     delete root;
 88     root=NULL;
 89 }
 90 
 91 
 92 template <class T>
 93 void Visit(T &x)
 94 {
 95     cout<<x<<"  ";
 96 }
 97 //先序遍历
 98 template<class T>
 99 void BinaryTree<T>::PreOrder(void (*Visit)(T &x),BTNode<T> *t)
100 {
101     if(t)
102     {
103     Visit(t->element);
104       PreOrder(Visit,t->lchild);
105     PreOrder(Visit,t->rchild);
106     }
107 }
108 template <class T>
109 void BinaryTree<T>::PreOrder(void (*Visit)(T &x))
110 {
111     PreOrder(Visit,root);
112 
113 }
114 
115 //中序遍历
116 template <class T>
117 void BinaryTree<T>::InOrder(void (*Visit)(T &x))
118 {
119     InOrder(Visit,root);
120 
121 }
122 template<class T>
123 void BinaryTree<T>::InOrder(void (*Visit)(T &x),BTNode<T> *t)
124 {
125     if(t)    
126     {
127     InOrder(Visit,t->lchild);
128     Visit(t->element);
129     InOrder(Visit,t->rchild);
130     }
131 }
132 //后序遍历
133 template <class T>
134 void BinaryTree<T>::PostOrder(void (*Visit)(T &x))
135 {
136     PostOrder(Visit,root);
137 
138 }
139 template<class T>
140 void BinaryTree<T>::PostOrder(void (*Visit)(T &x),BTNode<T> *t)
141 {
142     if(t)    
143     {
144     PostOrder(Visit,t->lchild);
145     PostOrder(Visit,t->rchild);
146     Visit(t->element);
147     }
148 }
149 
150 template<class T>                  //求二叉树的结点数
151 int BinaryTree<T>::Size()
152 {
153     return Size(root);
154 }
155 template<class T>
156 int BinaryTree<T>::Size(BTNode<T>*t)
157 {
158     if(!t)
159         return 0;
160     else return Size(t->lchild)+Size(t->rchild)+1;
161 }
162 
163 
164 template<class T>
165 int BinaryTree<T>::Node_num(BTNode<T>*p)   //叶子结点
166 {
167     if(p)
168     {
169         if(p -> lchild == NULL && p -> rchild == NULL)
170             return 1;
171         else
172             return Node_num(p -> lchild) + Node_num(p -> rchild);
173     }
174     else
175         return 0;
176 }
177 
178 template<class T>
179 BTNode<T>* BinaryTree<T>::Copy(BTNode <T>*t)       // 复制一棵二叉树
180 {
181     if(!t)
182         return NULL;
183     
184         BTNode<T>* q=new BTNode<T>(t->element);
185     q->lchild=Copy(t->lchild);
186     q->rchild=Copy(t->rchild);
187     return q;
188 
189 }
190 template<class T>
191 int BinaryTree<T>::High(BTNode<T>*p)  //高度
192 {
193     if(p == NULL)
194         return 0;
195     else if(p -> lchild == NULL && p -> rchild == NULL)
196         return 1;
197     else
198         return (High(p -> lchild) > High(p -> rchild) ? High(p -> lchild) + 1 : High(p -> rchild) + 1);
199 }
200 
201 template<class T>
202 void BinaryTree<T>::Exchange(BTNode<T>* &t)    //左右子树交换
203 {
204     if(t)
205     {
206         BTNode<T>*q = t -> lchild;
207         t -> lchild = t->rchild;
208         t -> rchild = q;
209         Exchange(t -> lchild);
210         Exchange(t -> rchild);
211     }
212 }
213 
214 int main ()
215 {
216     BinaryTree<char> a,b,x,y,z,temp;
217     char e;
218 
219     y.MakeTree(‘E‘,a,b);
220     z.MakeTree(‘F‘,a,b);
221     x.MakeTree(‘C‘,y,z);
222     y.MakeTree(‘D‘,a,b);
223     z.MakeTree(‘B‘,y,x);
224     cout<<"z的先序遍历:";
225     z.PreOrder(Visit);
226 
227     cout<<endl<<"z的中序遍历:";
228     z.InOrder(Visit);
229     cout<<endl<<"z的后序遍历:";
230     z.PostOrder(Visit);
231     cout<<endl<<"结点数:"<<z.Size();
232     cout<<endl<<"z的高度:"<<z.High(z.root);
233     cout<<endl<<"z的叶子结点:"<<z.Node_num(z.root);
234     temp.root=temp.Copy(z.root);
235     cout<<endl<<"temp的先序遍历:";
236     temp.PreOrder(Visit);
237 
238     z.Exchange(z.root);
239     cout<<endl<<"z的左右字数交换后的先序遍历:";
240     z.PreOrder(Visit);
241 
242     
243     z.BreakTree(e,y,x);
244     z.PreOrder(Visit);       //无输出
245 //    x.PreOrder(Visit);
246     cout<<endl<<"z的高度:"<<z.High(z.root);
247     cout<<endl<<"z的叶子结点:"<<z.Node_num(z.root);
248     cout<<endl;
249     return 0;
250 }